Authors: | Coja-Oghlan, Amin Ergür, Alperen A. Gao, Pu Hetterich, Samuel Rolvien, Maurice |
Title: | The rank of sparse random matrices |
Language (ISO): | en |
Abstract: | We determine the asymptotic normalized rank of a random matrix A over an arbitrary field with prescribed numbers of nonzero entries in each row and column. As an application we obtain a formula for the rate of low-density parity check codes. This formula vindicates a conjecture of Lelarge (2013). The proofs are based on coupling arguments and a novel random perturbation, applicable to any matrix, that diminishes the number of short linear relations. |
Subject Headings: | Finite field Random constraint satisfaction Random matrices Rank Sparse matrices |
URI: | http://hdl.handle.net/2003/42342 http://dx.doi.org/10.17877/DE290R-24179 |
Issue Date: | 2022-04-23 |
Rights link: | https://creativecommons.org/licenses/by/4.0/ |
Appears in Collections: | LS 02 Komplexitätstheorie und Effiziente Algorithmen |
Files in This Item:
File | Description | Size | Format | |
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Random Struct Algorithms - 2022 - Coja‐Oghlan - The rank of sparse random matrices.pdf | DNB | 2.29 MB | Adobe PDF | View/Open |
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